Intel Arc A310. They’re $100, support AV1 and powered completely by the PCIe bus. Combine it with Tdarr and you can compress your media library down to half the size easily while still being able to easily stream to any device you have.
Nearly any SBC you’d buy would beat the pants off it. If you’re shopping by price then check out a Libre Computer Sweet Potato or Renegade, or a Friendly Elec NanoPi R2S+. They’re <=$40 and should be able to run at least the services you mentioned. If you have more budget, there are $100 mini PCs on Amazon that are great for self hosting tons of stuff, like a Bmax B1 Pro.
Something headless for just running containers? Alpine.
It’s small, boots fast, simple, can run from RAM and Docker is available in its software repository.
An HP Elitedesk mini PC would be small enough to tuck away somewhere and have hardware accelerated transcoding support. Jellyfin recently enabled hardware acceleration for the latest Rockchip boards like the Orange Pi 5 so that’s an option too. If you pre-encode your media into a format compatible with everything you want to stream to then it doesn’t matter, just pick any hardware than can get on your network and run Linux.
Deploy code-server and either connect to it with a VPN or open the port needed to connect over the internet.
Traditional RAID isn’t very flexible and is meant/easiest for fresh disks without data. Since you’ve already got data in place, look into something like SnapRAID.